Atomistic insight into the initial stage of graphene formation on SiC(0001) surfaces

We present an atomistic insight into the processes leading to the formation of graphene on SiC(0001) surfaces by resorting to first-principles molecular dynamics empowered by free-energy sampling methods. Based on the experimental surface, consisting of terraces bordered by a sequence of steps, we find that Si atoms are dislodged from step edges and migrate toward more stable sites on the terrace, leaving behind C atoms carrying unsaturated chemical bonds. Our investigations reveal that subsequent Si atoms removal acts as a trigger to the formation of stable C-C bonds among these unsaturated C sites. This process eventually leads to the formation of C clusters which merge into larger structures with the typical pattern of graphene flakes. Specifically, a ${\mathrm{C}}_6$ ring formed during our simulations, assumes the typical hexagonal structure of graphene, becoming a precursor of larger graphene nanostructures. The characterization of the mechanisms and related free-energy landscapes provide an insight into the fundamental processes responsible for the realization of ordered C-based building blocks of graphene on the SiC(0001) surface.

Figure 1

Free-energy profile of Si desorption from the step edge and major relevant configurations. The color code for the atoms is blue for Si and brown for C. The bottom three atomic layers are not shown for clarity. The collective variable (see text for details) is the distance between a desorbing Si (red sphere) and the center of mass (black sphere) of the lower terrace site formed by three C atoms.

Figure 2

Free-energy landscape for a second Si desorption from the step edge, accompanied by the formation of a C-C bond and related stable configurations. The two CVs used are the distance between the desorbing Si atom (green sphere) and the COM of three C atoms on the lower terrace (site 1, black sphere), and the distance between the edge C atom (magenta sphere) and the COM of three C atoms on the upper terrace (site 2 underneath the green sphere). One C-C bond is formed in (E) and a C-C and a Si-Si bond appear in (F).

Figure 3

Free-energy landscape and related stable configurations for the second Si desorption along with the formation of three C-C bonds. Reaction paths 1 and 2 are highlighted as black dashed and solid lines.

Figure 4

Free-energy landscape (bottom left) and minimum free-energy reaction pathway (path1 $+$ path2 $+$ path3: dotted, solid, and dashed lines, respectively) for the clustering of carbon atoms. The labels from (I) to (VI) in the landscape indicate the positions of the (meta) stable configurations along the pathway. The free-energy profile along the identified pathway is given in Fig. S7 of the SM [41]. The stable configurations (I) and (VI) are shown in the top left and the bottom right, respectively. In (I), ${\mathrm{C}}_5$ and ${\mathrm{C}}_4$ clusters are highlighted with magenta and green spheres, respectively. Those clusters become a single cluster ${\mathrm{C}}_9$ in the final configuration (VI). The CV1 is the distance between the COM of ${\mathrm{C}}_5$ (left black sphere) and COM of ${\mathrm{C}}_4$ (right black sphere) and the CV2 is the distance between the COM of ${\mathrm{C}}_5$ and a C atom (yellow sphere).